Problem: $f(t) = -3t^{2}-5t-3(g(t))$ $h(x) = -6x^{2}+6x$ $g(n) = -3n-3(h(n))$ $ h(g(1)) = {?} $
First, let's solve for the value of the inner function, $g(1)$ . Then we'll know what to plug into the outer function. $g(1) = (-3)(1)-3(h(1))$ To solve for the value of $g$ , we need to solve for the value of $h(1)$ $h(1) = -6(1^{2})+(6)(1)$ $h(1) = 0$ That means $g(1) = (-3)(1)+(-3)(0)$ $g(1) = -3$ Now we know that $g(1) = -3$ . Let's solve for $h(g(1))$ , which is $h(-3)$ $h(-3) = -6(-3)^{2}+(6)(-3)$ $h(-3) = -72$